A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

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1 Waves_P2 [152 marks] A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. The beam is incident normally on a double slit. The distance between the slits is mm. A screen is at a distance D from the slits. The diffraction angle θ is labelled. 1a. A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed. [3 marks] 1b. The wavelength of the beam as observed on Earth is nm. The separation between a dark and a bright fringe on the screen is [2 marks] 4.50 mm. Calculate D.

2 The air between the slits and the screen is replaced with water. The refractive index of water is c. Calculate the wavelength of the light in water. [1 mark] 1d. State two ways in which the intensity pattern on the screen changes. [2 marks] A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. The beam is incident normally on a double slit. The distance between the slits is mm. A screen is at a distance D from the slits. The diffraction angle θ is labelled. 2a. Outline why the beam has to be coherent in order for the fringes to be visible. [1 mark]

$The graph of variation of intensity with diffraction angle for this experiment is shown. 2b.$

3 The graph of variation of intensity with diffraction angle for this experiment is shown. 2b. Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures. [3 marks] 2c. Deduce, in mm, the width of one slit. [2 marks]

4 The wavelength of the light in the beam when emitted by the galaxy was nm. 2d. Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth. [2 marks] A large cube is formed from ice. A light ray is incident from a vacuum at an angle of 46 to the normal on one surface of the cube. The light ray is parallel to the plane of one of the sides of the cube. The angle of refraction inside the cube is 33. 3a. Calculate the speed of light inside the ice cube. [2 marks]

5 Show that no light emerges from side AB. 3b. [3 marks] 3c. Sketch, on the diagram, the subsequent path of the light ray. [2 marks] Each side of the ice cube is 0.75 m in length. The initial temperature of the ice cube is 20 C. 3d. Determine the energy required to melt all of the ice from 20 C to water at a temperature of 0 C. Specific latent heat of fusion of ice = 330 kj kg 1 Specific heat capacity of ice = 2.1 kj kg 1 k 1 Density of ice = 920 kg m 3 [4 marks]

6 3e. Outline the difference between the molecular structure of a solid and a liquid. [1 mark] 4a. Outline what is meant by the principle of superposition of waves. [2 marks] 4b. Red laser light is incident on a double slit with a slit separation of 0.35 mm. A double-slit interference pattern is observed on a screen 2.4 m from the slits. The distance between successive maxima on the screen is 4.7 mm. [3 marks] Calculate the wavelength of the light. Give your answer to an appropriate number of significant figures.

7 4c. Explain the change to the appearance of the interference pattern when the red-light laser is replaced by one that emits green light. [2 marks] 4d. One of the slits is now covered. Describe the appearance of the pattern on the screen. [2 marks]

8 A student investigates how light can be used to measure the speed of a toy train. Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train. The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor. Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs. 5a. [3 marks] 7

9 5b. The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10 7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum. [1 mark] 5c. Estimate the speed of the train. [2 marks] 5d. In another experiment the student replaces the light sensor with a sound sensor. The train travels away from a loudspeaker that is emitting sound waves of constant amplitude and frequency towards a reflecting barrier. [2 marks] The sound sensor gives a graph of the variation of output voltage with time along the track that is similar in shape to the graph shown in the resource. Explain how this effect arises.

10 Two microwave transmitters, X and Y, are placed 12 cm apart and are connected to the same source. A single receiver is placed 6a. 54 cm away and moves along a line AB that is parallel to the line joining X and Y. [4 marks] Maxima and minima of intensity are detected at several points along AB. (i) Explain the formation of the intensity minima. (ii) The distance between the central maximum and the first minimum is 7.2 cm. Calculate the wavelength of the microwaves.

11 6b. Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna. [2 marks] An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.

12 6c. The receiving antenna becomes misaligned by 30 to its original position. [3 marks] The power of the received signal in this new position is 12 µw. (i) Calculate the power that was received in the original position. (ii) Calculate the minimum time between the wave leaving the transmitting antenna and its reception.

13 A longitudinal wave is travelling in a medium from left to right. The graph shows the variation with distance x of the displacement y of the particles in the medium. The solid line and the dotted line show the displacement at t=0 and t=0.882 ms, respectively. The period of the wave is greater than ms. A displacement to the right of the equilibrium position is positive. State what is meant by a longitudinal travelling wave. 7a. [1 mark] 7b. Calculate, for this wave, (i) the speed. (ii) the frequency. [4 marks]

14 The equilibrium position of a particle in the medium is at x=0.80 m. For this particle at t=0, state and explain 7c. (i) the direction of motion. [4 marks] (ii) whether the particle is at the centre of a compression or a rarefaction.

15 Monochromatic light is incident normally on four thin, parallel, rectangular slits. The graph shows the variation with diffraction angle θ of the intensity of light I at a distant screen. I 0 is the intensity of the light at the middle of the screen from one slit. 8a. Explain why the intensity of light at θ=0 is 16I 0. [3 marks]

16 8b. The width of each slit is 1.0µm. Use the graph to (i) estimate the wavelength of light. [4 marks] (ii) determine the separation of two consecutive slits. 8c. The arrangement is modified so that the number of slits becomes very large. Their separation and width stay the same. (i) State two changes to the graph on page 20 as a result of these modifications. (ii) A diffraction grating is used to resolve two lines in the spectrum of sodium in the second order. The two lines have wavelengths nm and nm. Determine the minimum number of slits in the grating that will enable the two lines to be resolved. [4 marks] 9a. (i) Calculate the speed of this wave. (ii) Show that the angular frequency of oscillations of a particle in the medium is ω= rads 1. [4 marks]

17 One particle in the medium has its equilibrium position at x=1.00 m. 9b. (i) State and explain the direction of motion for this particle at t=0. [4 marks] (ii) Show that the speed of this particle at t=0.882 ms is 4.9ms 1.

18 The travelling wave in (b) is directed at the open end of a tube of length 1.20 m. The other end of the tube is closed. 9c. (i) Describe how a standing wave is formed. [3 marks] (ii) Demonstrate, using a calculation, that a standing wave will be established in this tube.

19 This question is about the properties of waves. Microwaves from a microwave transmitter are reflected from two parallel sheets, A and B. Sheet A partially reflects microwave energy while allowing some to pass through. All of the microwave energy incident on sheet B is reflected. Sheet A is fixed and sheet B is moved towards it. While sheet B is moving, the intensity of the signal detected at the receiver goes through a series of maximum and minimum values. Outline why a minimum in the intensity occurs for certain positions of sheet B. 10a. [3 marks]

20 The apparatus is arranged to demonstrate diffraction effects. 10b. [3 marks] The microwaves emerge from the transmitter through an aperture that acts as a single slit. (i) Outline what is meant by diffraction. (ii) A maximum signal strength is observed at P. When the receiver is moved through an angle θ, a first minimum is observed. The width of the aperture of the transmitter is 60 mm. Estimate the value of θ. Microwaves can be used to demonstrate polarization effects. Outline why an ultrasound receiver and transmitter cannot be used 10c. to demonstrate polarization. [2 marks]

21 This question is about the motion of a ship and observing objects from it. A security camera on the ship captures an image of two green lamps on the shore. The lamps emit light of wavelength 520 nm. 11a. [3 marks] The camera has a circular aperture of diameter 6.2 mm. The lamps are separated by 1.5 m. Determine the maximum distance between the camera and the lamps at which the images of the lamps can be distinguished. The sailors on the ship wear polarized sunglasses when observing the sea from the ship. Unpolarized light from the Sun is incident on the sea. Describe the polarization of the sunlight that is reflected from the sea. 11b. [2 marks]

22 Outline how polarized sunglasses help to reduce glare from the sea. 11c. [3 marks] This question is about the superposition of waves. State what is meant by the principle of superposition of waves. 12a. [1 mark]

23 The diagram shows two point sources of sound, X and Y. Each source emits waves of wavelength 1.1 m and amplitude A. Over 12b. the distances shown, any decrease in amplitude can be neglected. The two sources vibrate in phase. [5 marks] Points O and P are on a line 4.0 m from the line connecting X and Y. O is opposite the midpoint of XY and P is 0.75 m from O. (i) Explain why the intensity of the sound at O is 4A 2. (ii) Deduce that no sound is detected at P.

24 This question is about polarization. Unpolarized light is directed towards two polarizers. The dashed lines represent the transmission axes of the polarizers. The angle θ between the transmission axes of the polarizers is initially 0 º. On the axes below, sketch a graph to show how the intensity I of the light emerging from the second polarizer varies with θ. 13. [2 marks] This question is about polarization. State what is meant by polarized light. 14a. [1 mark]

Unpolarized light is incident on the surface of a plastic. The angle of incidence is θ. The reflected light is viewed through an 14b. analyser whose transmission axis is vertical.

25 Unpolarized light is incident on the surface of a plastic. The angle of incidence is θ. The reflected light is viewed through an 14b. analyser whose transmission axis is vertical. [2 marks] The variation with θ of the intensity I of the transmitted light is shown in the graph. Explain why there is an angle of incidence, for which the intensity of the transmitted light is zero.

26 14c. Unpolarized light from a source is split, so that there is a path difference of half a wavelength between the two beams. [4 marks] A lens brings the light to focus at point P on a screen. The lens does not introduce any additional path difference. State and explain whether any light would be observed at P, in the case in which the polarizers have their transmission axes (i) parallel. (ii) at right angles to each other.

27 This question is about simple harmonic motion (SHM), wave motion and polarization. A liquid is contained in a U-tube. 15a. [7 marks] The pressure on the liquid in one side of the tube is increased so that the liquid is displaced as shown in diagram 2. When the pressure is suddenly released the liquid oscillates. The damping of the oscillations is small. (i) Describe what is meant by damping. (ii) The displacement of the liquid surface from its equilibrium position is x. The acceleration a of the liquid in the tube is given by the expression a = 2g l x where g is the acceleration of free fall and l is the total length of the liquid column. Explain, with reference to the motion of the liquid, the significance of the minus sign. (iii) The total length of the liquid column in the tube is 0.32m. Determine the period of oscillation.

28 The string in (c) is fixed at both ends and is made to vibrate in a vertical plane in its first harmonic. 15b. [6 marks] (i) Describe how the standing wave in the string gives rise to the first harmonic. (ii) Outline how a travelling wave in a string can be used to describe the nature of polarized light.

29 This question is about sound. A source emits sound of frequency f. The source is moving towards a stationary observer at constant speed. The observer measures the frequency of the sound to be f. (i) Explain, using a diagram, why f is greater than. 16a. f (ii) The frequency f is 275 Hz. The source is moving at speed 20.0 ms 1. The speed of sound in air is 330 ms 1. Calculate the observed frequency f of the sound. [5 marks]

30 A source of sound is placed in front of a barrier that has an opening of width comparable to the wavelength of the sound. 16b. [4 marks] A sound detector is moved along the line XY. The centre of XY is marked O. (i) On the axes below, sketch a graph to show how the intensity I of the sound varies as the detector moves from X to Y. (ii) State the effect on the intensity pattern of increasing the wavelength of the sound.

31 16c. (i) Outline the difference between a polarized wave and an unpolarized wave. (ii) State why sound waves cannot be polarized. [3 marks] This question is in two parts. Part 1 is about a lightning discharge. Part 2 is about microwave radiation. Part 2 Microwave radiation A microwave transmitter emits radiation of a single wavelength towards a metal plate along a line normal to the plate. The radiation is reflected back towards the transmitter. A microwave detector is moved along a line normal to the microwave transmitter and the metal plate. The detector records a sequence of equally spaced maxima and minima of intensity. Explain how these maxima and minima are formed. 17a. [4 marks]

32 The microwave detector is moved through 130 mm from one point of minimum intensity to another point of minimum intensity. On the way it passes through nine points of maximum intensity. Calculate the (i) 17b. (ii) wavelength of the microwaves. frequency of the microwaves. [4 marks] Describe and explain how it could be demonstrated that the microwaves are polarized. 17c. [3 marks] International Baccalaureate Organization 2018 International Baccalaureate - Baccalauréat International - Bachillerato Internacional Printed for HAEF (Psychico College)

A longitudinal wave travels through a medium from left to right.

1. This question is about simple harmonic oscillations. A longitudinal wave travels through a medium from left to right. Graph 1 shows the variation with time t of the displacement x of a particle P in